Question

Luke and Dana are making cookies for the Westland pantry. they only have up to six hours to bake! they can bake 32 chocolate chips in an hour(x) and 20 snickerdoodles in an hour(y) they need to make at least a hundred fifty cookies which one of these are a valid selectionA 5,1B 2,8C 3,2D 1,4

Answer 1

Let x be the number of hours to bake chocolate chip cookies.

Let y be the number of hours to bake snickerdoodles.

They only have up to six hours to bake (means equal or less than 6)

`x+y\le6\quad eq.1`

They can bake 32 chocolate chips in an hour(x) and 20 snickerdoodles in an hour(y) and also they need to make at least a hundred fifty cookies. (at least means equal or greater than)

`32x+20y\ge150\quad eq.2`

Now let us substitute each of the given options into the above two inequalities and check which option satisfies them

Option A: (x, y) = (5, 1)

`\begin{gathered} x+y\le6 \\ 5+1\le6 \\ 6\le6\quad \text{pass} \end{gathered}`
`\begin{gathered} 32(5)+20(1)\ge150 \\ 160+20\ge150 \\ 180\ge150\quad \text{pass} \end{gathered}`

As you can see option A satisfies both of the inequalities therefore, option A is a valid selection.

Note: You can try other options and you will notice that none of them will satisfy both inequalities.